Hello, I have a 1998 E300 turbodiesel with a bizarre braking problem.

With the engine running, the brake pedal feels normal, doesn't require much effort to push, braking performance is fine. It feels totally normal.

After I shut the engine off, the brake pedal turns into a rock. You cannot push it down, not even a little bit. Upon starting the engine again, the brake pedal goes back to its normal feeling regular state.

In a healthy car, engine off, if you pump the brake pedal a few times, it slowly becomes stiffer and stiffer until you can no longer depress the pedal. My car feels this way every time you shut the engine off - it goes directly to the rock hard state without pumping the pedal.

Sounds like some kind of weird vacuum issue, but the fact that everything feels normal and fine with engine running has me stumped.

Any ideas on what to check are much appreciated.